Finite-temperature Density Matrix Renormalization Group Research Articles

Finite-temperature density matrix embedding theory

We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding on the 1D Hubbard model both at half-filling and away from it, and the 2D Hubbard model at half-filling, comparing to exact data where available, as well as results from finite-temperature density matrix renormalization group, dynamical mean-field theory, and dynamical cluster approximations. The accuracy of finite-temperature density matrix embedding appears comparable to that of the ground-state theory, with at most a modest increase in bath size, and competitive with that of cluster dynamical mean-field theory.

Finite-temperature correlations in a quantum spin chain near saturation

Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the $S=1/2$ Heisenberg spin chain compound K$_2$CuSO$_4$Cl$_2$ at several temperatures in a magnetic field near saturation. Critical correlations characteristic of the predicted $z=2$, $d=1$ quantum phase transition occurring at saturation are shown to be consistent with the observed neutron spectra. The data is well described with a scaling function computed using a free fermion description of the spins, valid close to saturation, and the corresponding scaling limits. One of the most prominent non-universal spectral features of the data is a novel thermally activated longitudinal mode that remains underdamped across most of the Brillouin zone.

Reducing the numerical effort of finite-temperature density matrix renormalization group calculations

Finite-temperature transport properties of one-dimensional systems can be studied using the time dependent density matrix renormalization group via the introduction of auxiliary degrees of freedom which purify the thermal statistical operator. We demonstrate how the numerical effort of such calculations is reduced when the physical time evolution is augmented by an additional time evolution within the auxiliary Hilbert space. Specifically, we explore a variety of integrable and non-integrable, gapless and gapped models at temperatures ranging from T = ∞ down to T/bandwidth = 0.05 and study both (i) linear response where (heat and charge) transport coefficients are determined by the current–current correlation function and (ii) non-equilibrium driven by arbitrary large temperature gradients. The modified density matrix renormalization algorithm removes an ‘artificial’ build-up of entanglement between the auxiliary and physical degrees of freedom. Thus, longer time scales can be reached.

Magnetic properties of a S = 1/2zigzag spin chain compound (N2H5)CuCl3

We present a theoretical and experimental study of aquasi-one-dimensional zigzag antiferromagnet (N2H5)CuCl3,which can be viewed as weakly coupled Heisenberg chains with a frustratedinteraction. We first discuss generic features of the magnetic properties of thezigzag spin chain between the nearly single chain case and the nearly double chaincase, on the basis of the finite temperature density-matrix renormalization group(DMRG) calculations. We next show the experimental results for the magneticsusceptibility and the high-field magnetization of a single crystal of (N2H5)CuCl3above the Néel temperature TN = 1.55 K.By comparing the experimental data with the DMRG results carefully, we finallyobtain the ratio of the nearest and next-nearest exchange couplings asJ1/J2 = 0.25with J2/kB = 16.3 K.We also investigate the three-dimensional (3D) couplingJ′ effect byusing mean-field theory combined with the DMRG calculations. The estimated value J′ ∼ 0.04J2supports the one-dimensionality of (N2H5)CuCl3above TN.

Kondo hole in one-dimensional Kondo insulators

Properties of a nonmagnetic impurity in Kondo insulators are investigated by considering a one-dimensional Kondo lattice model with depletion of a localized spin. The ground-state phase diagram determined by the Lanczos method shows that the magnetic moment is more stable than in ordinary metals. Temperature dependence of impurity susceptibilities is also studied by using the finite-temperature density-matrix renormalization group.

Finite-temperature phase diagram of mixed-stack charge-transfer complexes

The mixed-stack organic charge-transfer complex, (BEDO–TTF)(Cl 2TCNQ), has shown a phase transition accompanied with a sharp drop in the magnetic susceptibility and with an increase in the intermolecular overlap, as the temperature is lowered. Here, we theoretically consider the possibility for a phase transition from the ionic phase to a neutral phase, which is driven by charge-transfer fluctuations. Using finite-temperature density-matrix renormalization-group calculations for the one-dimensional extended Hubbard model with alternating potentials, we show that, with increasing transfer integral t, a transition from the neutral phase to the ionic phase is induced by spin fluctuations for small t, while another transition from the ionic phase to the neutral phase is induced by charge-transfer fluctuations for large t. Near the phase boundary, the free energy is easily lowered by dimerization of transfer integrals or by staggered magnetic field. Thus, a further transition is also possible to a dimerized nonmagnetic phase or to an antiferromagnetic phase at a lower temperature. In two dimensions, we expect that the effect of charge-transfer fluctuations is larger and that the transition to the dimerized nonmagnetic phase is suppressed.

Magnetic Phases and Long-Range Ordering of the Haldane System in High Magnetic Fields

Critical properties of field-induced magnetic phases are investigated in the one-dimensional S = 1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.

Efficiency of Asymmetric Targeting for Finite-TDMRG

Two targeting schemes have been known for the density matrix renormalization group (DMRG) applied to non-Hermitian problems; one uses an asymmetric density matrix and the other uses symmetric density matrix. We compare the numerical efficiency of these two targeting schemes when they are used for the finite temperature DMRG.

Erratum: Temperature-Induced Gap Formation in Dynamic Correlation Functions of the One-Dimensional Kondo Insulator: Finite-Temperature Density-Matrix Renormalization-Group Study [Phys. Rev. Lett. 81, 4939 (1998)

Erratum: Temperature-Induced Gap Formation in Dynamic Correlation Functions of the One-Dimensional Kondo Insulator: Finite-Temperature Density-Matrix Renormalization-Group Study [Phys. Rev. Lett. 81, 4939 (1998)

Temperature-Induced Gap Formation in Dynamic Correlation Functions of the One-Dimensional Kondo Insulator: Finite-Temperature Density-Matrix Renormalization-Group Study

Combination of the finite-temperature density-matrix renormalization group and the maximum entropy presents a new method to calculate dynamic quantities of one-dimensional many-body systems. In the present paper, density of states, local dynamic spin, and charge correlation functions of the one-dimensional Kondo insulator are discussed. Excitation gaps open with decreasing temperature and the gaps take different values depending on channels. The excitation spectra change qualitatively around the characteristic temperature corresponding to the spin gap which is the lowest energy scale of the Kondo insulator.